Chinese Science Bulletin

, Volume 58, Issue 30, pp 3704–3708 | Cite as

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

  • Ullah Asad
  • GuoQuan Liu
  • Hao Wang
  • Khan Matiullah
  • Faraz Khan Dil
  • Iqbal M Zubair
Open Access
Article Materials Science


A new grain topology-size relationship in three-dimensional (3D) polycrystalline microstructures has recently been established by considering the effects of non-random first nearest neighbor grains. In this contribution, a generalized form for this relationship is presented by considering the interactions of kth (k=1, 2, 3…) nearest neighbor grains, and large scale Monte Carlo-Potts model simulation is used to investigate the general neighborhood topological effect on the topology-size relationship. The results show that, unlike their first nearest neighbors (k=1), the topological correlations of 3D grains with their kth layers (k⩾2) of nearest-neighbors may have trivial effect on the topology-size relationship.


polycrystalline microstructures grain size grain topology neighbors topological correlations 


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Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Ullah Asad
    • 1
    • 2
  • GuoQuan Liu
    • 1
    • 3
  • Hao Wang
    • 1
  • Khan Matiullah
    • 1
    • 4
  • Faraz Khan Dil
    • 1
    • 4
  • Iqbal M Zubair
    • 5
  1. 1.School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.Department of MathematicsKarakoram International University Gilgit-BaltistanGilgitPakistan
  3. 3.State Key Laboratory for Advanced Metals and MaterialsUniversity of Science and Technology BeijingBeijingChina
  4. 4.Department of PhysicsUniversity of Science and Technology BannuBannuPakistan
  5. 5.School of Applied SciencesUniversity of Science and Technology BeijingBeijingChina

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